In uncertainty theory, quadratic entropy is a type of entropy that provide a quantitative measurement of the uncertainty of uncertain variables. This paper presents the maximum entropy principle for quadratic entropy of uncertain variables, that is, out of all the uncertainty distributions satisfying given constraints, choose the maximum quadratic entropy one.

Non-deductive reasoning systems are often representation dependent, representing the same situation in two different ways may cause such a system to return two different answers. This is generally viewed as a significant problem. For example, the principle of maximum entropy has been subjected to much criticism due to its representation dependence. There has, however, been almost no work invest...

We find a new formula for the limit of the capacity of certain sequences of multidimensional semiconstrained systems as the dimension tends to infinity. We do so by generalizing the notion of independence entropy, originally studied in the context of constrained systems, to the study of semiconstrained systems. Using the independence entropy, we obtain new lower bounds on the capacity of multid...

This paper provides evidence for Genzel and Charniak’s (2002) entropy rate principle, which predicts that the entropy of a sentence increases with its position in the text. We show that this principle holds for individual sentences (not just for averages), but we also find that the entropy rate effect is partly an artifact of sentence length, which also correlates with sentence position. Second...

Absrmez-Jaynes’s principle of m@mum entropy and KuUba&‘s priodple of min imum cromentropy (mhlmum dire&d dfvergenoe) are shown tobeunfquelycomxtmethodsforhductiveinf~whennewinformnt ionlsghninthefomlofexpe&edvalues.ReviousjILstit icatioaslLve htuiUvearguma@andrelyonthepro~ofentropyanderossenhppy lasinfmersmes.‘Illeapproarbben?that reasoMble methodsofhductiveinfere~shouidleedto~nsistentresuitswh...

Copulas are a general way of describing dependence between two or more random variables. When we only have partial information about the dependence, i.e., when several different copulas are consistent with our knowledge, it is often necessary to select one of these copulas. A frequently used method of selecting this copula is the maximum entropy approach, when we select a copula with the larges...

We establish lower bounds for the entropy of the Hard Core Model on a few 2d lattices L. In this model the allowed configurations inside {0,1} are the one’s in which the nearest neighbor 1’s are forbidden. Our method which is based on a sequential fill-in scheme is unbiassed and thereby yields in principle arbitrarily good estimates for the topological entropy. The procedure also gives some det...

A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n ≤ m, and the task is relatively straightforward for well-defined functional relationships. For example, if Y1 and Y2 are independent random variables, each uniform on [0, 1], one can deter...